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The Giants did not have a lot of salary cap space, so this offseason was always going to be about the draft for them. Anything else they added was likely come out of the bargain bin of free agency.

And their bargain shopping is about to begin.

Starting on Tuesday, the Giants figure to be in the market for a right tackle, maybe an edge rusher, and probably plenty of depth, when the free-agent signing period heats back up again. That's the first day that free-agent signings do not count against the NFL's compensatory draft pick formula, which determines comp picks for the next draft, and takes into account free agent signings, losses, money spent and performance. Any player a team signs Tuesday won't count against his new team.

That's good news for a Giants team that is still trying to stockpile draft picks for the future and has only about $14 million in salary cap space left. Considering they also have to sign a 10-player draft class, including three first-rounders, that doesn't leave the Giants much for a spending spree.

But here's a look at some of the players they still could get:

RT Mike Remmers

This has felt like an inevitable signing for months. The former Viking, who was coached in Minnesota by then-offensive coordinator Pat Shurmur, has already visited the Giants and his agent has stayed in touch. Shurmuer and Remmers seem like a good match, but the delay here has more to do with the fact that the 30-year-old, 6-5, 310-pounder is still recovering from back surgery. When the Giants are satisfied with his recovery, they could offer him a deal and a chance to start.

LB Shane Ray

The Giants feel fairly comfortable with their edge-rushing situation with free agent Markus Golden and second-year pro Lorenzo Carter. They also have high hopes for third-round pick Oshane Ximines, though he may be a year away coming out of Old Dominion. But while they're accumulating promising, young players, it's worth a look at the 6-3, 245-pound Ray, who turns 26 in two weeks. A former first-round pick, he had eight sacks in 2016. If he's recovered from the wrist injury that ruined his last two seasons, he could be a steal.

DE Ziggy Ansah

He doesn't quite fit into their youth movement, but the 6-5, 275-pounder is simply the best available pass rusher on the market, even coming off a shoulder injury. After trading Olivier Venon, the Giants don't have many players with a resume of pass-rushing success. Ansah, who had 12 sacks in 14 games in 2017, would easily fill that void. The Giants probably don't have enough cap room to sign him, but it's worth a call.

RT Jermy Parnell

OK, the last Jaguars offensive lineman they signed (Patrick Omameh) didn't work out so well, and Parnell will turn 33 in July and is coming off a knee injury. But the Giants still need a right tackle and there aren't many on the market. If he's healthy, this 6-6, 326-pounder is at least experienced. He had been entrenched as the Jaguars starter, with 57 starts over the last four years.

RB Jay Ajayi

The Giants' offense is now the Saquon Barkley show, but they still can't give him every carry and they do have to be prepared if … you know … something happens. And the new regime has not appeared to be completely comfortable with Wayne Gallman as the backup. Ajayi would be a risk coming off a torn ACL, but a one-year deal would give him a chance to prove he's healthy and work his way back with limited carries. The Giants probably only need him for a series or two per game. And if he's able to give them that, the 25-year-old would be one of the most talented backup running backs in the league.

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